High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus

Paolo Baldi, Gérard Kerkyacharian, Domenico Marinucci and Dominique Picard

Journal of Multivariate Analysis, 2008, vol. 99, issue 4, 606-636

Abstract: We prove a multivariate CLT for skewness and kurtosis of the wavelets coefficients of a stationary field on the torus. The results are in the framework of the fixed-domain asymptotics, i.e. we refer to observations of a single field which is sampled at higher and higher frequencies. We consider also studentized statistics for the case of an unknown correlation structure. The results are motivated by the analysis of high-frequency financial data or cosmological data sets, with a particular interest towards testing for Gaussianity and isotropy.

Keywords: High; frequency; asymptotics; Wavelets; Random; fields; Multivariate; Central; Limit; Theorem; Tests; for; Gaussianity; and; isotropy (search for similar items in EconPapers)
Date: 2008
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